Let's rewrite the given equation step-by-step:
1. We start with the given quadratic equation:
[tex]\[
x^2 + 10x + 25 = 0
\][/tex]
2. Notice that [tex]\( x^2 + 10x + 25 \)[/tex] looks like a perfect square trinomial. Recall the standard form of a perfect square trinomial:
[tex]\[
(a + b)^2 = a^2 + 2ab + b^2
\][/tex]
3. In our case, if we let [tex]\( a = x \)[/tex] and [tex]\( b = 5 \)[/tex], then:
[tex]\[
(x + 5)^2 = x^2 + 2(x)(5) + 5^2 = x^2 + 10x + 25
\][/tex]
4. Therefore, we can rewrite the original equation as:
[tex]\[
(x + 5)^2 = 0
\][/tex]
Thus, the equation [tex]\( x^2 + 10x + 25 = 0 \)[/tex] can be rewritten as:
[tex]\[
(x + 5)^2 = 0
\][/tex]
This completes the transformation.
